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lukranit [14]
3 years ago
12

You mix the letters A, C, Q, U, A, I, N, T, A, N, C, E throughly. Without looking you select one letter. Find the probability of

each event. Write your answer as a fraction.
1) P(T)
2) P(A)
3) P(vowel)
4) P(N)
Mathematics
1 answer:
kvv77 [185]3 years ago
4 0
1. 1/12
2. 3/12
3. 6/12
4. 2/12

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Rewrite the following in the form log(c).<br> log (2) + log(3)
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Answer:

log (6)

Step-by-step explanation:

because by product property of logs

log (2)  + log(3) = log (2*3) = log (6)

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Solve this problem.
Katyanochek1 [597]

Answer:

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Step-by-step explanation:

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Evaluate using integration by parts ​
PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

I(n)=\displaystyle\int x^ne^x\,\mathrm dx

One round of IBP, setting

u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx

\mathrm dv=e^x\,\mathrm dx\implies v=e^x

gives

\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx

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This is called a power-reduction formula. We could try solving for I(n) explicitly, but no need. n=5 is small enough to just expand I(5) as much as we need to.

I(5)=x^5e^x-5I(4)

I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)

I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)

I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)

I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))

Finally,

I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C

so we end up with

I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C

I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C

and the antiderivative is

\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C

8 0
3 years ago
X over 7+4 is greater than or equal to 16
Blizzard [7]

X/11>=16

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5 0
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Find p(2) and p(4) for the function p(x) = 6x4 + 4x3 – 3x2 + 8x + 15.
gulaghasi [49]

Answer:

p(2) =147 and p(4) = 1791

Step-by-step explanation:

We are given p(x)= 6x^4 + 4x^3 – 3x^2 + 8x + 15.

Now we need to find value of p(2) and p(4)

Put x =2,

p(2) = 6(2)^4 + 4(2)^3 – 3(2)^2 + 8(2) + 15

p(2) = 6(16)+4(8)-3(4)+8(2)+15

p(2) = 96+32-12+16+15

p(2) = 147

Now put x = 4

p(4) = 6(4)^4 + 4(4)^3 – 3(4)^2 + 8(4) + 15

p(4) = 6(256)+4(64)-3(16)+8(4)+15

p(4) = 1536+256-48+32+15

p(4) = 1791

3 0
4 years ago
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